A cylinder has inner and outer radii of $2 c m$ $2 cm$ and $5 c m$ $5 cm$ , respectively, and a mass of $8 k g$ $8 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $6 H z$ $6 Hz$ to $8 H z$ $8 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-02-26T09:26:42

The change in angular momentum is $= 0.15 k g m^{2} s^{- 1}$ $=0.15kgm^2s^-1$

The angular momentum is $L = I ω$ $L=Iomega$

where $I$ $I$ is the moment of inertia

For a cylinder, $I = m \frac{r_{1}^{2} + r_{2}^{2}}{2}$ $I=m(r_1^2+r_2^2)/2$

So, $I = 8 \cdot \frac{{0.02}^{2} + {0.05}^{2}}{2} = 0.0116 k g m^{2}$ $I=8*(0.02^2+0.05^2)/2=0.0116kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

$Delta omega=(8-6)*2pi=4pirads^-1$

$DeltaL=0.0116*4pi=0.15kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 5 cm5cm5 cm, respectively, and a mass of 8 kg8kg8 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 6 Hz6Hz6 Hz to 8 Hz8Hz8 Hz, by how much does its angular momentum change?